"TL;DR: Carl Fredricksen died in his sleep the night after he returns from court with the order that he vacate to a retirement home (as a result of the incident with the construction worker and the mailbox). Everything that happened afterwards represents Carl's journey through the Afterlife.
The first thing we need to do is disprove the whole floating house thing as that sets the stage for the rest of the characters. We already know that the amount of balloons Carl used to rip his house off its foundation and sail to South America was far smaller than it needed to be in order to accomplish that goal. So right away the idea of balloon-floating a house becomes unlikely.
We also know that other constraints would have made the effort impossible. Based on the information in the above article he would have needed at least 100,000 balloons, each three feet across. That's hardly something that a senior citizen on a fixed income could have afforded to locate, purchase, and have delivered in a few hours. Then there's the matter of the 1.5 million cubic feet of helium needed to fill those balloons; again, not enough time or money to locate, purchase, and deliver. And he certainly didn't have it on hand. At best, he could have raided the welding supply shed in the adjacent construction site for a fraction of the helium he'd need, but even so there's no way he would be able to haul all of those canisters into his house by himself. Also, there were only a few helium canisters outside the house, certainly far less than he would have needed, so where did it all come from?
But let's assume for a moment that he could have somehow gotten the balloons and the helium (and the string) into his house with nobody noticing. He gets his court order and decides to take action. He's got 24 hours at best — 86,400 seconds — to inflate and tie off his 100,000 balloons. Can't be done. The world's fastest balloon inflater couldn't do it, let alone a probably-arthritic 78-year-old man. And since all of his neighbors are long gone he doesn't have anyone to help him out, so how did that get done? Plus, we saw in the movie that he had all of the balloons covered in a tarp. How could he have secured the tarp down so well that all those balloons — theoretically enough to rip a house off its foundation — didn't also pull the tarp out of its moorings?
So all combined, the raising of the house represents Carl's initial transition from the physical world to the spiritual world. He "rises up" in the same way as people who have near-death experiences relate the feeling of floating above their body and watching as the doctors resuscitate it.
Russell represents Carl's guardian angel, or perhaps more accurately a 'spiritual guide' of sorts who is trying to 'earn his wings' by helping Carl with his transition. Russell has earned many badges and is very close to getting his final badge, thus "earning his wings". His final badge requires him to help a senior citizen. This makes sense; Russell's other badges were preparing him in various ways for the final test, which is to help a senior citizen into the afterlife. Once Russell earns that badge his 'training' is complete and he becomes a true guardian angel. Russell's innocence and devotion shows his purity, and the example he sets through that purity helps Carl see the error in his ways of thinking. Several times in the movie you see Carl change his actions in direct response to Russell's response/actions.
Kevin (the bird) represents a Higher Calling — a Muse, perhaps, or maybe even God itself. Something that Carl can aspire to that's beyond his own desires and wishes. Russell would be fully aware of what Kevin is. At first Carl couldn't care less about Kevin and wants to leave it behind, but Russell eventually shows Carl some of the better aspects of Kevin. Kevin's love of chocolate is a metaphor for the small rewards that are earned along the way of pursuing a higher calling. The fact that Kevin is rarely around when Carl needs him and often around when Carl doesn't want him to be is also indicative of a higher calling. A Muse-like inspiration rarely strikes when we want it to. By the end of the movie Carl has come to accept and protect Kevin, and thereby accepting his own higher purpose in life (and afterwards) even if he doesn't fully understand it.
We know that Dug's "translation collar" is impossible even in the context of the movie's reality so there's another clue that what's happening on screen isn't really happening in the movie's reality. It's just another part of Carl's transition. But Dug (the dog) himself represents a metaphor for Transition, the change from one state to the other. Dug was Muntz's dog but switched to Carl/Russell's side. Dug was the bottom ranking dog but became Alpha. And through the translation collar Dug bridged the gap between animal and human — in the same way that Dug is helping Carl to bridge the gap between life and afterlife.
Muntz is Evil, of course, resplendent upon a story of lies at first and commanding the Hounds of Hell. Muntz wants to destroy Kevin for his own glory and personal satisfaction in much the same way that Lucifer wants to destroy all that is good (biblically speaking). Carl's soul is the prize here; if Muntz destroys the Higher Calling then Carl falls into despair, and Muntz wins.
The house itself represents Carl's attachment to the physical world with Paradise Falls being Carl's perceived representation of Heaven. And with the house finally landing at Paradise Falls, Carl has finally finishing his transition and completed his greatest adventure, presumably reuniting with Ellie in Heaven."